JPH01503012A - Digital integration module for sampling controllers - Google Patents

Abstract

(57) [Summary] This bulletin contains application data before electronic filing, so abstract data is not recorded.

Description

[Detailed description of the invention] The present invention is an integral module capable of negative feedback for a sampling control device, A recursive form in which the relationship between the force signal and the output signal is formed from each sample. It concerns an integral module determined by an integral algorithm.

Microcomputer stands out in terms of high processing speed and large memory and address space. The use of data forms the technical basis for the realization of high-capacity regulation systems. death However, the assumption of complete availability of such a calculator is A sufficiently accurate physical/mathematical description of the controlled object in the form of a so-called “model” .

As is well known, the dynamic behavior between the input and output of a controlled object is divided into two types: Differential equations of various orders derived based on consideration of physical laws occurring within the system It is described by a set of formulas and regular equations.

We will provide a unified mathematical description of such a set of equations, and based on that, we will develop an appropriate Formally standardized down to control strategy design and layout In recent control technology, two main methods have been developed to process Ta. One of them is the well-known “frequency domain method”, in which the system equation is Moved from time domain to frequency domain. Dynamic system behavior is complex in this way. The design and layout of the corresponding control system in the form of transfer functions is Can be processed continuously.

A second, less popular method for a unified mathematical description is the so-called This is a system representation in “state space”. In this case, generally having various orders System equations are a set of first-order differential equations in the time domain with appropriate definitions of state quantities. will be moved to All inputs, outputs and state quantities of the system are then advantageously −i through one so-called “system, input, output and transition matrix” can be grouped into vectors that are connected to each other. by matrix calculation Along with this simple mathematical processing of the system description, one of the state space representations is Another advantage is that the equation of state is normalized under the assumptions of linearity and time invariance. can be transferred to the so-called "normal form" by a transformation. These are certainly Each describes the same physical system and thereby describes the dynamic system in each case. However, specific structural properties of the object to be modeled, e.g. For example, it appears particularly clearly in one of its eigenvalues. The canonical form is controlled by constitutes one particularly suitable starting point for the design of strategies and regulator structures. . Thus, for example, the current state of one concrete system is Simulation is performed using an “observer” that models the system by “trailing” inside the computer. Since this “internal” state of the system can be accessed and can be influenced by regulatory effects. Known regular forms are, for example, the so-called “jigilda” ``observer and control normal forms'' and various ``observer and control normal forms''.

The system description by an equation of state or its representation in a selected normal form is Another advantage is that it can be implemented particularly well within analog and digital computers. has. This system description is jJj! 1! block-oriented This is made possible by leading to a modular system representation. 1 technical pair The number of such “blocks” needed to model an image depends on the existing system. directly related to the order and thus each to one modified “system order” of one or more blocks in a way that makes it easy to adapt the range of the required canonical form. Other benefits in the technical realization of this system description that are possible by addition or omission. A point is one in which all blocks in one of the normal forms are constructed identically and The aim is to obtain one integrator in each core during the representation in the time domain. It was like this For example, one target model constructed according to the Jordan-normal form is A number of separate negative feedback loops are provided with coefficient setters, corresponding to the system order. It consists of a parallel connection of integrators. Complex system behavior is thus reduced to the first order. Simulated by superposition of system reactions. Accordingly, one object - or control - one target model constructed according to the normal form in each case of the number corresponding to the system order, all of which are negatively fed back through a common coefficient setter It consists of a series connection of integrators. Also, the complex system behavior here is first-order Synthesized from reactions in lower-level systems.

Such a target model or an “observer” based on it can be integrated into one digital Sl! as a component during the actual technical configuration in a section or automated device. The integrator required for It is known that In this case, the current value of the input quantity at each sampling point is detected, and then detected or calculated at the previous sampling point and The currently stored quantities are used to determine the current output value. simulate an integrator In known algorithms for "Rules" is a common cause of resentment.In response to this, the relational expression %formula% Here, vk = output signal Vh-+ at the first sampling point: -1st sample Output signal uh-+ at the time of pulling: Input signal at the -1st sampling time TA: Sampling time T, binomial separator time constant holds true. This relational expression is, for example, based on Norbert and Hoffmann (Norbert H. offmann) N, “Digital adjustment by microprocessor (Digi tale Regelung lll1t Mikroprozessor)'' , VV Eg Publishing, 1983, pages 23 et seq. In the above formula Therefore, a “square rule integrator module” that operates recursively is capable of negative feedback, Therefore, for example, when representing the state space of a technical system, in the above normal form, It has the advantage that it can be used as a component of However, on the other hand, The shape rule integrator module has the disadvantage that it performs I-approximation only with a constant average area error. Has a point. Furthermore, for example, sampling time k1 (Vh-+ = uv- +=0) upon starting of such an integrator module the output signal V.

is the first subsequent sampling time point after the passage of one sampling time TA The first sampled input value uk-1 is -1 at the previous sampling point. The results obtained by the TA/TI evaluation are particularly disadvantageous. This happened again For example, in an observation- or control-observer constructed according to a normal form, After a change in the input signal has passed a number of sampling times commensurate with the order of the system. The first time it has passed through all the integrator modules connected in series, and the It has the disadvantage that it all "arrives" at the output of the observer. in this way The constructed target model must thereby take into account considerable reaction times. Minimum simulation of the square rule integrator module is required to maintain stability. Each sampling time T, where there is a symmetric time constant to rate, is less than It turns out that both must be larger by a factor of 2.

There are two ways to make such a modular automation system dynamic. is possible. In one method, the sampling time is a sufficiently small integral time constant is set with observance of the above ratio to the current magnitude of the sampling time T, It can be made as small as possible. Such a method is useful for sampling control systems. The sampling time of the system is limited by its internal configuration and organization, and For accuracy reasons, such systems generally already have a maximum possible configurable sample. It provides negative material to be operated in a short time.

Other methods for dynamizing sampling control systems are or allow a more desirable ratio between the integration time constant and the respective sampling time present. The key is to use highly capable algorithms. In particular, systems using state-space methods In describing, which - means. In other words, the area under one continuous function is calculated using the so-called “trapezoidal rule”. ``closer'' (this is known).The integral algorithm formed from this is It is significantly more powerful than known square rule algorithms, and Gang, Ratzel (-8lfgangII Latzel), “Process Compilation” Adjustment by computer r)'', P, ■, V7 Senschaft Publishing, 1977, especially pages 79-91. Are listed.

In other words, for the integral algorithm based on the trapezoidal rule, the relational expression % expression %) T: sampling time TI: Integrator time constant ■k: Output signal u at the first sampling point,: Input signal at the second sampling point Force signal u*-+: During this period, the input signal at the -1st sampling point holds true. From the equation, it can be seen that at the start of the algorithm, for example, immediately at the sampling point, At this moment the values v,−1 and uk−1 are still obtained from the previous sampling. Even if not, it can be seen that the output value d0・u should be taken into consideration. . Therefore, in contrast to the integration algorithm based on the square rule, the integration algorithm based on the trapezoidal rule The algorithm "reacts" fairly quickly to changes in the input signal.

Furthermore, the average area error during numerical integration according to the trapezoidal rule is always equal to zero; On the other hand, the average area error during numerical integration using the square rule is the sampling time It has been found that it increases with

For example, in a modular target model composed of a known regular form, A prerequisite for using an integral module is its arbitrary interconnectability and Especially the possibility of negative feedback. On the other hand, it is structured by the trapezoidal rule and operates recursively. The integrating module that operates is not capable of negative feedback, which means that changes in the input value are not delayed. directly to the output value as a so-called “pass-through value” and thus again via negative feedback. It is based on acting on input values immediately without any delay. Nevertheless When negative feedback of the trapezoidal rule integral module is attempted, for calculation of the current output value The formula that requires the output value itself to be calculated first at each sampling point is arise. Therefore, a meaningful and feasible algorithm for processing the individual summands of this expression system order does not exist. When forced negative feedback of such elements in the computer would cause the recursive computation to immediately break down, but the algorithmic continuation The basic prerequisite for the discretization of a digital system is exactly this at the sampling point. lies in the recursive computability of .

The problem of the present invention is that the internal recursive processing algorithm is formed by an approximation of It is an object of the present invention to provide an integral module that can provide negative feedback while maintaining

According to the invention, this problem is achieved by the measures specified in the characterizing part of claim 1. will be resolved. Further advantageous embodiments of the invention are listed in the subclaims.

Brief description of the drawing Hereinafter, the present invention will be explained in more detail with reference to the drawings. When I explain the drawing to an oil bug, Figure 1 shows the so-called “observer-regular form” that operates recursively according to the trapezoidal rule. Fig. 2 shows another modification of the module in Fig. 1. Fig. 3 is another modified structural diagram of the module in Fig. 2, and Fig. 4 is a structural diagram of the module in Fig. 2. Example of negative feedback of the integral module according to the trapezoidal rule in Fig. 2 or 3 by Akira , FIG. 5 is another embodiment of an integral module using a trapezoidal rule capable of negative feedback according to the present invention. , Figure 6 shows the general structure of an n-th order target model composed of “observer-normal form”. Construction, FIG. 7 shows “ This is an example of a third-order target model configured with "observer normal form".

Figure 1 shows the structure based on the “observer normal form” and the trapezoidal rule. shows a known structure of an integral module that operates recursively. That clearly It is known from the theory of linear sampling control, and is also the basis of the so-called "two-conversion" Complex “movement operator” used as The elements in Figure 1, represented by is a memory or dead time element. This element is input as -1 at the sampling time. Read the value Vk-, +d0・uk-1 given at the end, and use this at the time of sampling. TA for the duration of the TA, and also for the last subsequent sampling time. The above integration algorithm using the 0 trapezoidal rule that outputs the value a at the output terminal is as follows. can be expressed as follows based on the display in FIG.

vIl=a+DW Vh = (Vh-+ +do °uk-1) +d6 °uk where DW: passing price As mentioned above, the output signal value Vk of this trapezoidal rule integral module is directly dependent on the input signal The present invention eliminates the possibility of negative feedback of this element, which cannot be negatively fed back to u6. In order to achieve this while maintaining "input-output behavior", first see Figure 2 and It may be advantageous to make some of the internal structural changes shown in FIG.

That is, in the first step the structure of FIG. 1 on the one hand no longer outputs the signal v, The output signal a of the dead time element 1/z can be added to the addition point A1. No more negative feedback The input value uk is now multiplied by a coefficient 2 as compensation for the passing value DW=d,・uk. and is supplied to addition point A1. The equi-individualities in Figures 1 and 2 are added in both cases. Value for score A1 d,'uh +a+da・u.

can be easily recognized from the fact that it is supplied with The part surrounded by chain lines in Figure 2 corresponds to one “square rule integral module” composed of square rules. That is clear.

Another modification is shown in Figure 3, where the dashed line in Figure 2 is the calculation formula. were combined into one overall element. Furthermore, the passing value within the channel DW and the direction The amplification factor d0 located in the input channel of the regular integral module is were grouped into input quantity channels for direct evaluation. Thus, based on the previous transformation Therefore, the structure shown in Figure 1 shows that the overall structure behaves invariably like a trapezoidal regular integral module. One passing value channel DW is provided so as to operate according to the rectangular rule. Disassembled into one internal part.

According to the invention, the structure shown in FIG. 3 of another trapezoidal rule integral module structure, but nevertheless one recursive algorithmic process only takes one sample. negative feedback as possible within the system. For this purpose, according to the invention For example, in the first step, only the part of the structure shown in Figure 3 that can be negatively fed back is subjected to negative feedback. Ru. As mentioned above, the square rule integration module is capable of negative feedback without restriction.

For this reason, according to FIG. 4, the output of the internal rectangular integral module IIIE is separated. It serves as a negative feedback output terminal AR. In this way, when the negative feedback branch RZ is required, From this output terminal AR, a great invention is generated via a negative feedback amplifier that prepares an evaluation coefficient. Connected to the input end of the trapezoidal rule integral module. In the second step, this During negative feedback, between the original output signal V and the signal at the negative feedback output terminal AR. The deviations present in , are compensated for. There are many possibilities for this. According to figure 4 One possibility is shown in an embodiment of the invention. At that time, the intermediate that received negative feedback (The passing value DW not included in fa is the internal rectangular rule integral module 2/ (z-1) and is multiplied by the evaluation coefficient present in the negative feedback branch RZ. It is then fed back to the input end of the trapezoidal rule integral module according to the invention.

The embodiment of the invention according to FIG. 5 includes a trapezoidal regular integral module air 2 according to the invention Another signal for correcting the deviation of the signal at the negative feedback output terminal AE from the output signal V of Possibility has been shown. At that time, the correction is performed by applying the first amplifier VE to the input signal U. This is done directly by appropriate selection of the evaluation coefficients provided through. This is in Figure 4 Let the coefficients d0 and h of the elements VB and VE" of the separated negative feedback loop of It arises by combining the

Figure 6 shows, as an example, a time domain constructed in the so-called “observer-regular form”. The general structure of the nth order object model in the region is shown. As mentioned above, this is n The evaluation coefficients S, b, . ...b□1 is fed with the evaluated input signal U. Furthermore, the input signal U is It is evaluated by the coefficient d as a “pass value” and is directly passed through the integrator via the summing point Sn. The output signal is superimposed on the column circuit output signal MA (1), and thereby the output signal is Contributes to the formation of V. The signal matrix w, (t) at the output end of the integrator chain is a coefficient -ao, al...-am-1 for each integrator 1. ．． 1. Negative feedback is given to the mixing point 5O1S1...5(n-1) at the input terminal of . It can be seen that all integrators are provided with negative feedback. To the present invention The trapezoidal rule integral module capable of negative feedback is based on the target model according to the principle diagram in Figure 6. In the practical realization of Particularly suitable for the role of

Figure 7 shows an option using a trapezoidal rule integral module capable of negative feedback, which is a major invention. An advantageous embodiment of a third-order object model in server-normal form is shown. this The model is three trapezoidal regular integral modules tyz+,! ? □2, ■A2. series of It consists of a circuit. All integrators are connected to the negative feedback output A of the third integration module. The coefficient ao, in the manner described in the general example of FIG. 6 using the signal at R3. Negative feedback is provided via al and at. The output signal of each integral module The third module It□, corrects the deviation of the signal at the negative feedback output from the signal. A more detailed explanation will be given by way of example. According to the embodiment shown in FIG. Correction is performed by setting appropriate coefficient values in amplifier VE31. d.

Here h=a=+aI"do+30・do", the amplification coefficient is This results in the sum of the amplification factors of the three negative feedback branches. The first negative feedback branch is It directly extends from the output end of the third integrator to the input end, and also includes an amplification coefficient a. There is. The second negative feedback branch connects indirectly to the second integrator I from the output of the third integrator. via the pass value of tz* to the input of the third integrator, and the amplification factor -a Contains l and do. Finally, the third negative feedback branch starts from the output of the third integrator. Indirectly the first and second integrators ITRI, TT2! extends through the passing value of It also includes amplification coefficients -ao.d,.d.

°The corrections in the other integral modules I, □l, lT□ are different from the embodiment shown in FIG. It is always done in a similar way. At that time, the negative feedback output terminal AR3 of the third integrator The input signal is evaluated via amplifiers VE12, VE22 and sent to the respective integral module. superimposed on the output end of the module. At that time, the amplification coefficient of the amplifier is the relational formula % formula % Set according to.

From the structure according to Figure 7, the three states attached to it I　X11%　X21sX31 is directly converted into the trapezoidal rule integral module 1 according to the invention by means of the conversion network T. □１、■ Negative feedback output #4A of 1□2, It□3 From the signals at R1, AR2, AR3 Can be simulated. at the respective negative feedback output from the original output signal. A conversion network T for the first and second integrators to correct deviations between the signals. Among them, the evaluation coefficients known from amplifiers VE12 and VE22 are considered together. must be

The minimum time constant of interest to be simulated to maintain stability is the rectangular rule integral module. Unlike the rules, each sampling time T! ! is more than 0.5 times All that is required is the characteristic of the trapezoidal rule integral module capable of negative feedback according to the present invention. Another advantage of the zero-flame module is that the system to be modeled Regularly structured state space with the assumption of linearity of the system - in normal form Not only can it be used for the configuration of the target model or observer, but also Therefore, nonlinear structures can also be modeled in a way that is individually adapted to the given conditions that exist. It is structured in a modular manner.

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Claims (3)

[Claims] 1. An integral module capable of negative feedback for a sampling control device, the input signal being At each sampling point, the relationship between determined by a recursive integration algorithm that is formed by approximating the area under an integral module, a) The relationship between the input signal and the output signal is determined using the square rule at each sampling point. The recursive integration algorithm is formed by approximating the area under a continuous function. An integral module containing an internal rectangular rule integral module (IRE) to be determined. b) the input signal (u*) of the integration module (ITZ) is the first coefficient d o=TA/2・T1 Here, TA: sampling time T1: Integral time constant and the input signal to the internal rectangular rule integral module (IRE) The first amplifier (VE, VE 11, VE21, VE31) and c) Pass value (DW*) and internal as output signal (v) of integral module (ITZ) form the sum of the doubled output signal (a*) of the rectangular regular integration module (IRE). d) an internal rectangular rule integral module (IRE); a separate negative feedback output terminal (AR) from which an output signal (a*) that is doubled; e) In the presence of negative feedback from the negative feedback output end to the input end of the integrating module (ITZ) In order to correct the deviation of the signal at the negative feedback output terminal (AR) from the output signal (v) of means (VE*, VE, VE31, VE22, VE12) An integral module capable of negative feedback for a sampling control device, characterized in that it includes: (Figures 4, 5 and 7). 2. Negative feedback signal at the output from the output signal at the output of the integration module As a means to correct the deviation of the passing value (DW) by a second coefficient (h), The first signal is evaluated, also inverted and superimposed on the input signal (u) of the integration module (ITZ). 2 amplifiers (VE*), where the second coefficient (h) is the integral module. The negative feedback branch (RZ) extends from the negative feedback output terminal (AR) of the loop (ITZ) to the input terminal. ), the integral module according to claim 1, (Figure 4). 3. Corrects the deviation of the signal at the negative feedback output from the output signal of the integration module. The first coefficient of the first amplifier (VR, VE31) is expressed by the relational expression do/I+h・do where h: amplification coefficient in the negative feedback branch (RZ) of the integral module (1TZ) The integral module according to claim 1, characterized in that the integral module is selected according to the and Figure 7).